To convert an oscillator output of 10MHz to a desired frequency of 1MHz using a synchronous counter, we can follow the steps outlined below:

1. **Understanding Synchronous Counters:**
Synchronous counters are a type of digital circuit that can be used to divide the frequency of an input signal by a specific factor. They consist of flip-flops and logic gates. Each flip-flop represents a bit, and the logic gates determine how the flip-flops are connected to create the desired counting sequence.

2. **Selecting the Counter Type:**
There are various types of synchronous counters available, such as binary counters, decade counters, and modulo-n counters. For this scenario, a binary counter is suitable as it can divide the frequency by a power of 2.

3. **Determining the Counter Size:**
The counter size is determined by the number of flip-flops required to achieve the desired frequency division. In this case, since we want to divide the frequency from 10MHz to 1MHz, a counter size of 4 bits is sufficient. This is because 2^4 = 16, and dividing 10MHz by 16 gives us the desired 1MHz frequency.

4. **Connecting the Counter:**
To connect the counter, the output of the 10MHz oscillator is connected to the clock input of the first flip-flop. The output of each flip-flop is connected to the clock input of the next flip-flop. This creates a cascaded connection, allowing the frequency to be divided by the factor determined by the counter size.

5. **Programming the Counter:**
To program the counter for the desired frequency division, the initial state of the flip-flops needs to be set. The counter is typically designed to reset back to the initial state after reaching its maximum count. Since we want to divide by 16, the counter needs to count up to 15 (1111 in binary). Therefore, the initial state should be set to 0000, and the counter will count from 0000 to 1111 and then reset back to 0000.

6. **Obtaining the Desired Frequency:**
With the counter connected and programmed, the output of the counter will now provide the desired frequency of 1MHz. The output is taken from the most significant bit (MSB) of the counter, as it changes state at a frequency equal to the input frequency divided by the counter size.

By using a 4-bit synchronous counter, the output frequency can be divided from 10MHz to 1MHz, satisfying the requirement for the circuit.